Question # 3:
If $\hat{Y}$ is the estimator of Y, given that:
$\hat{Y} = g(X) = aX + b$
Show that the minimum mean square error $e_{MSE} = \sigma_Y^2(1 - \rho_{XY}^2)$,
where $\sigma_{XY} = cov(X, Y)$ and $\rho_{XY}$ is the correlation coefficient of X and Y.